Arithmetic of Higher-Dimensional Algebraic Varieties

One of the great successes of twentieth century mathematics has been the remarkable qualitative understanding of rational and integral points on curves, gleaned in part through the theorems of Mordell, Weil, Siegel, and Faltings. It has become clear that the study of rational and integral points has deep connections to other branches of mathematics: complex algebraic geometry, Galois and étale cohomology, transcendence theory and diophantine approximation, harmonic analysis, automorphic forms, and analytic number theory.

This text, which focuses on higher dimensional varieties, provides precisely such an interdisciplinary view of the subject. It is a digest of research and survey papers by leading specialists; the book documents current knowledge in higher-dimensional arithmetic and gives indications for future research. It will be valuable not only to practitioners in the field, but to a wide audience of mathematicians and graduate students with an interest in arithmetic geometry.

• Cohomology
• Dimension
• Diophantine approximation
• Grad
• algebra
• algebraic geometry
• algebraic varieties
• number theory

"These articles which are written by leading experts make interesting reading and also give the non expert reader an idea of the subject.  In addition there is an extensive index covering the entire volume and a glossary of important notions.  In particular readers who are not specialists in the field may find this very helpful."

---Monatshefte für Mathematik

• Department of Mathematics, University of California, Berkeley, Berkeley, USA

  Bjorn Poonen

• Mathematisches Institut, Göttingen, Germany

  Yuri Tschinkel

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